I am unable to get the deflection of beam correctly and the plot is incorrect.Even when i am using the right code. Also i tryed to distribute my beam into sections.

% Plot the bending of a beam with rectangular cross section

% The cross section is in the plane of y-z

% The longitudinal axis of the beam is parallel to the x axis

scale=50;

E= 1.999*10^11; % N/m2

nu = 0.3;

I= 7.74.*10^-7; % m^4

H = 0.0762;% m

R1 = 2224; % N

R2 = 2224; % N

P = 2224; % N

L = 3.0; % m

L1= 0.91; % m

L2= 2.09; %m

N=20;

x=(0:L/N:L);

DIM =size(x);

y= zeros(DIM);

figure(1)

plot(x,y,'.-')

axis equal

hold on

xlabel('Distance(m)')

ylabel('vertical deformation (m)')

title('Deformation of a beam')

xd=x;

yd=y;

for ii=1:length(x)

v=(1/E*I).*(2224*x(ii).^3/6)-(2208.021*x(ii)-(2224*(x(ii)-L1).^3/6)...

-(2224*(x(ii)-L2).^3/6));

yd(ii) = y(ii)+scale.*v;

end

figure(1)

plot(xd,yd,'o-')

axis equal

hold on

[Chuguang Pan]

The plot like a sine curve, maybe the code to calculate the deflecction of beam is incorrect.

Answer 1

[VBBV]

scale = 50;
E=  1.999*10^11; % N/m2
nu = 0.3;
I= 7.74.*10^-7; % m^4
H = 0.0762;% m 
R1 = 2224; % N
R2 = 2224; % N
P = 2224; % N
L = 3.0; % m 
L1= 0.91; % m 
L2= 2.09; %m
N=50;
x=(0:L/N:L);
DIM =size(x);
y= zeros(DIM);
% figure(1)
% plot(x,y,'.-')
% axis equal
% yyaxis right

xd=x;
yd=y;
for ii=1:length(x)
    v=(1/(E*I)).*((2224*x(ii)^3)/6-2208.021*x(ii)-(2224*(x(ii)-L1)^3)/6 ...
    -(2224*(x(ii)-L2)^3)/6);
    yd(ii) = y(ii)+scale.*v;
end
figure(1)
plot(xd,real(yd),'o-')
axis equal
xlabel('Distance(m)')
ylabel('vertical deformation (m)')
title('Deformation of a beam')

[VBBV]

The flexural stiffness term need to be put in the denominator of the equation. Remaining terms of the equations need to also checked with the signs for getting correct (simply supported) beam deflection values along its length.

[Vruddhi]

It is a simply supported beam with two point loads equidistant from the support. And i am new to use this software. Kindly share the code of solving deflection in sections. As the value of deflection at ends will be zero.

[VBBV]

The code which you shared in question is modified to give outputs as shown in this thread. If you run the code, you would get a deflection curve shown from modified code with correct values. To obtain defelction in sections you need to split the equation as below

scale = 50;
E=  1.999*10^11; % N/m2
nu = 0.3;
I= 7.74.*10^-7; % m^4
H = 0.0762;% m 
R1 = 2224; % N
R2 = 2224; % N
P = 2224; % N
L = 3.0; % m 
L1= 0.91; % m 
L2= 2.09; %m
N=50;
x=(0:L/N:L);
DIM =size(x);
y= zeros(DIM);
% figure(1)
% plot(x,y,'.-')
% axis equal
% yyaxis right

xd=x;
yd=y;
for ii=1:length(x)
    v=(1/(E*I)).*((2224*x(ii)^3)/6-2208.021*x(ii)-(2224*(x(ii)-L1)^3)/6 ...
    -(2224*(x(ii)-L2)^3)/6);
    yd(ii) = y(ii)+scale.*v;
    v1(ii) = (1/(E*I)).*(2224*x(ii)^3)/6;  % section 1
    v2(ii) = (1/(E*I)).*(-2208.021*x(ii)); % section 2
    v3(ii) = (1/(E*I)).*(-2224*(x(ii)-L1)^3)/6; % section 3
    v4(ii) = (1/(E*I)).*(-2224*(x(ii)-L2)^3)/6; % section 4
end
disp([v1.', v2.', v3.', v4.'])

         0         0    0.0018    0.0219
    0.0000   -0.0009    0.0015    0.0200
    0.0000   -0.0017    0.0012    0.0183
    0.0000   -0.0026    0.0009    0.0167
    0.0000   -0.0034    0.0007    0.0152
    0.0001   -0.0043    0.0005    0.0137
    0.0001   -0.0051    0.0004    0.0124
    0.0002   -0.0060    0.0003    0.0112
    0.0003   -0.0069    0.0002    0.0100
    0.0004   -0.0077    0.0001    0.0089
    0.0005   -0.0086    0.0001    0.0079
    0.0007   -0.0094    0.0000    0.0070
    0.0009   -0.0103    0.0000    0.0062
    0.0011   -0.0111    0.0000    0.0054
    0.0014   -0.0120    0.0000    0.0047
    0.0017   -0.0128    0.0000    0.0040
    0.0021   -0.0137   -0.0000    0.0035
    0.0025   -0.0146   -0.0000    0.0029
    0.0030   -0.0154   -0.0000    0.0025
    0.0035   -0.0163   -0.0000    0.0021
    0.0041   -0.0171   -0.0001    0.0017
    0.0048   -0.0180   -0.0001    0.0014
    0.0055   -0.0188   -0.0002    0.0011
    0.0063   -0.0197   -0.0002    0.0009
    0.0072   -0.0206   -0.0004    0.0007
    0.0081   -0.0214   -0.0005    0.0005
    0.0091   -0.0223   -0.0007    0.0004
    0.0102   -0.0231   -0.0009    0.0002
    0.0114   -0.0240   -0.0011    0.0002
    0.0126   -0.0248   -0.0014    0.0001
    0.0140   -0.0257   -0.0017    0.0001
    0.0154   -0.0265   -0.0021    0.0000
    0.0170   -0.0274   -0.0025    0.0000
    0.0186   -0.0283   -0.0029    0.0000
    0.0203   -0.0291   -0.0035    0.0000
    0.0222   -0.0300   -0.0040   -0.0000
    0.0241   -0.0308   -0.0047   -0.0000
    0.0262   -0.0317   -0.0054   -0.0000
    0.0284   -0.0325   -0.0062   -0.0000
    0.0307   -0.0334   -0.0070   -0.0000
    0.0331   -0.0343   -0.0079   -0.0001
    0.0357   -0.0351   -0.0089   -0.0001
    0.0383   -0.0360   -0.0100   -0.0002
    0.0411   -0.0368   -0.0112   -0.0003
    0.0441   -0.0377   -0.0124   -0.0004
    0.0472   -0.0385   -0.0137   -0.0005
    0.0504   -0.0394   -0.0152   -0.0007
    0.0537   -0.0402   -0.0167   -0.0009
    0.0572   -0.0411   -0.0183   -0.0012
    0.0609   -0.0420   -0.0200   -0.0015
    0.0647   -0.0428   -0.0219   -0.0018

figure(1)
plot(xd,real(yd),'o-')
axis equal
xlabel('Distance(m)')
ylabel('vertical deformation (m)')
title('Deformation of a beam')